How can the constraint: if $x_1=1$ then $x_2+x_3\geq 1$ be written in linear programming if the variables $x_1,x_2,x_3$ are binary?
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2 Answers
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Here's a derivation via conjunctive normal form: \begin{equation} x_1 \implies (x_2 \lor x_3) \\ \neg x_1 \lor (x_2 \lor x_3) \\ (1 - x_1) + x_2 + x_3 \ge 1 \\ x_1 \le x_2 + x_3 \end{equation}
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$-x1 + x2 + x3 \geq 0 $
should be sufficient.
